Criminal Case is a case where an accused has allegedly committed a crime against an injured person, as for a instance, theft, fraud, etc., punishable under Criminal Law.
The injured person can decide whether to launch a complaint with the police, and a public prosecutor will prosecute the case, or the injured person may appoint his own lawyer to prosecute the case.
In such Criminal Case the injured person may want to claim damages from the accused. If so, then, the plaintiff, which is the public prosecutor or the injured person, have a right to claim for damages in that particular Criminal Case, simultaneously, i.e., the Civil Case relating to the Criminal Case.
In some circumstances, the injured party may file a separate Civil Case claiming for damages, rather than having Criminal Case and Civil Case combined in the same case.